DP Curves Research Articles

Dependence of pressure drop on surfactant solution flow rate in foam coreflooding experiments through 50 mD limestone

The pressure drop (dP) and apparent viscosity characterize the ability of foam to control gas mobility in core flooding experiments. There is no clarity regarding which factor, total flow rate (qt), foam quality (fg), gas (qg) or liquid (ql) flow rate, determines the dP. The inconsistency in interpretation can be caused by the differences in conditions of experiments, which are carried out at one fixed and other varying parameter. In this study, dP and length of foam drops at the outlet are measured in three types of experiments at 400 and 500 psi for comparison: 1) scans at fixed total flow rate and varying fg; 2) tests at fixed liquid flow rate and varying gas flow rates; 3) tests at fixed gas flow rate and varying liquid flow rates. In foam scans 1, the dP measured at two qt decreased almost linearly due to low foamability starting at fg = 0.3, indicating a high quality regime. The length of foam drops and the bubble size increased with the increase in fg. In tests 2 and 3, there was no direct relationship between dP and qg at a constant ql, but dP increased with increasing ql at constant qg, which is in line with other publications. In addition, there was no direct dependence of the foam texture on the increase in qg and ql. The discrepancy in the dependence of dP on ql and qg between the three experiments was due to the fact that different combinations of ql and qg used in tests 2 and 3 resulted in the same fg and qt, which led to data overlap and data distribution in both high and low regimes. Meanwhile, dP measured in all three experiments was a linear function of the liquid flow rate with a line slope equal to the outlet pressure, regardless of the total flow rate. Due to the mathematical expression, the equation dP = P · ql can be called the equation of ideal foam and used as a test case for further comparisons. Thus, ql is the governing factor in high quality regime for a given surfactant and conditions. The slopes were also equal to the outlet pressures for the dP curves as a function of qt in tests 2 and 3. Irrespective the linear correlation between dP and ql, the deviations were observed at medium values of foam quality at 400 psi. These deviations were accompanied by the simultaneous deviations in the length of foam drops, showing that they were of nonrandom nature. In some deviating points, the foam texture at the outlet changed abruptly and disproportionately to fg changes. This could be the evidence of the intermediate state between the coarse-foam and strong-foam. • The dP of foam flow is a linear function of liquid flow rate with a line slope equal to the outlet pressure. • Due to the mathematical expression, dP = P · ql can be called the equation of ideal foam. • Deviations from linear function at some points are caused by disproportionate changes in foam texture. • Transition foam quality is higher for foaming agents with higher initial viscosity.

Inter-segmental coordination of the spine is altered during lifting in patients with ankylosing spondylitis: A cross-sectional study.

The abnormal inter-segmental coordination of the spine during lifting could be used to monitor disease progression and rehabilitation efficacy in patients with ankylosing spondylitis (AS). This study aimed to compare the inter-segmental coordination patterns and variability of the spine during lifting between patients with AS (n = 9) and control (n = 15) groups.Continuous relative (CRP) and deviation (DP) phases between each segment of the spine (two lumbar and three thorax segments) and lumbosacral joint were calculated. The CRP and DP curves among participants were decomposed into few functional principal components (FPC) via functional principal component analysis (FPCA). The FPC score of CRP or DP of the two groups were compared, and its relationship with the indexes of spinal mobility was investigated.Compared with the control group, the AS patients showed more anti-phase coordination patterns in each relative upper spine segment and lumbosacral joint. In addition, either less or more variation was found in the coordination of each relative lower spine segment and lumbosacral joint during different time periods of lifting for these patients. Some cases were considerably related to spinal mobility.the inter-segmental coordination of the spine was altered during lifting in AS patients to enable movement, albeit inefficient and might cause spinal mobility impairment.

基于DP曲线构建PH样条

基于DP曲线构建PH样条

A Type of Cubic DP Curve with Shape Parameters

A Type of Cubic DP Curve with Shape Parameters

Multi-Degree Reduction of DP Curves with Constraints of Endpoints Continuity

In this paper, we presented a constrained multi-degree reduction algorithm of DP curves based on the transformation between the DP and Bézier curves. We first correct the conversion formula between Bernstein basis and DP basis. And then, we deal with multi-degree reduction of NP curves by degree reduction of Bézier curve.

Multiple degree elevation and constrained multiple degree reduction for DP curves and surfaces

In this paper, the problem of single and multiple degree elevation and reduction for DP curves and surfaces is considered and expressed in matrix representations. Using monomial matrix representations of the univariate DP polynomials, single and multiple degree elevation matrices can be derived by minor extension of this monomial matrix. Given this result, matrices of constrained single and multiple degree reduction can be readily obtained. Finally, important and sufficient conditions for degree reduction can also be found from these resulting matrices.

Representing conics by low degree rational DP curves

A DP curve is a new kind of parametric curve defined by Delgado and Pena (2003); it has very good properties when used in both geometry and algebra, i.e., it is shape preserving and has a linear time complexity for evaluation. It overcomes the disadvantage of some generalized Ball curves that are fast for evaluation but cannot preserve shape, and the disadvantage of the Bezier curve that is shape preserving but slow for evaluation. It also has potential applications in computer-aided design and manufacturing (CAD/CAM) systems. As conic section is often used in shape design, this paper deduces the necessary and sufficient conditions for rational cubic or quartic DP representation of conics to expand the application area of DP curves. The main idea is based on the transformation relationship between low degree DP basis and Bernstein basis, and the representation theory of conics in rational low degree Bezier form. The results can identify whether a rational low degree DP curve is a conic section and also express a given conic section in rational low degree DP form, i.e., give positions of the control points and values of the weights of rational cubic or quartic DP conics. Finally, several numerical examples are presented to validate the effectiveness of the method.

Electrochemical study of the dimerization of nicotinamide

The electrochemical behaviour of nicotinamide was studied by dc and DP polarography and linear sweep cyclic voltammetry in the pH range 3–7. DP polarograms were analyzed by using a curve-fitting procedure and equations given in the literature. From the analysis of the dc and DP curves, together the variations of the polarographic parameters with both the concentration and the drop-time, it can be concluded that the process consists of the electrodimerization of nicotinamide (through a radical—radical coupling taking place in the reaction layer), and the electroreduction of the radical formed after the first one-electron transfer. This last process takes place at more negative potentials and its rate is controlled by a chemical step placed after the electron transfers.

Study of the electrochemical reduction of nicotinic acid at a mercury electrode

A more comprehensive study than those reported previously in the literature has been carried out on the electrochemical reduction of nicotinic acid in aqueous solutions over a wide pH range. The influence of the pH, reactant concentration and drop time on the different polarographic and kinetic parameters in the two electroreduction processes involved is studied. Experimental DP curves and the theoretical profiles corresponding to different mechanisms are compared. The experimental results indicate that the process corresponding to the wave observed in very strong acid media involves two electron transfers followed by a protonation step yielding the corresponding nicotinic aldehyde. Two waves can be observed in the 0.5–5 pH range. The first corresponds to the dimerization of radicals produced in the first electron transfer via a radical-radical coupling in the reaction layer. The second originates from the reduction of these radicals, which competes with the dimerization step. The only wave observed in neutral and basic media corresponds to a dimerization analogous to that yielding the first wave observed in the pH range 0.5–5. The voltammetric results indicate that the dimer oxidizes at potentials very far from those at which it is formed. In any case, the presence of Triton X-100 inhibits the dimerization process. The C- E curves indicate that nicotinic acid is not appreciably adsorbed on the mercury surface at the working concentration.

Reduction of 2-cyclohexen-1-one in aqueous media on a mercury electrode

A more comprehensive study than those previously reported in the literature has been carried out on the electrochemical reduction of 2-cyclohexen-1-one in aqueous solutions over a wide pH range. The influence of the pH, reactant concentration and drop time on the different polarographic and kinetic parameters, such as the limiting current, half-wave potentials, Tafel slopes and reaction orders with respect to 2-cyclohexen-1-one and the H + ion, is studied for the two electroreduction processes involved. A comparison between experimental DP curves and theoretical profiles corresponding to different mechanisms is also included. The experimental results clearly indicate that the process corresponding to the first wave (pH < 8) involves the protonation of 2-cyclohexen-1-one at the carbonyl group, followed by an electron transfer to yield a neutral radical which dimerizes in the reaction layer. This dimerization step is the rds at potentials corresponding to the foot of the wave, whereas diffusion at 3 < pH < 5 and the previous protonation at pH > 7, govern the process at potentials corresponding to the top of the wave. Regarding the second wave (pH > 5), which is due to the reduction of the unprotonated form of 2-cyclohexen-1-one, a change of mechanism can be observed as the pH increases. This change is due to the fact that the dimerization step can take place via either neutral radical—neutral radical (RH π + RH π) or radical anion—radical anion (R π− + R π−) coupling, depending on both the pH and the concentration of proton donors in the solution.

VAPOUR PHASE GRAFTING OF VINYL MONOMERS ONTO RAYON BY CERIUM INITIATOR

Based on our experience of the vapour phase acetylation of cellulose, the vapour phase grafting of methyl acrylate, ethyl acrylate, methyl methacrylate and acrylonitrile onto viscose rayon pretreated by cerium ammonium nitrate solution were studied and the influence of the initiator and nitric acid concentration in the pretreating solution, atmospheric pressure in the reaction vessel, and reaction temperature upon the grafting were investigated. Some mechanical properties of the grafted rayon were measured. The results obtained are as follows:(1) For e. g. AN grafting, about 150% retention of the pretreating solution by the rayon is most favourable.(2) MA or EA grafting is the first order reaction, MMA the sigmoid, and AN the fibrous reaction controlled by diffusion.(3) Ultimate graft amount of each monomer shows the maximum in relation to the initiator and nitric acid concentration in the pretreating solution.(4) Ultimate graft efficiency of AN or MMA is about 90%, but that of MA or EA decreases linearly with the initiator concentration.(5) Ultimate graft amount of each monomer decreases with the increase of carbonyl content of the rayon when the initiator concentration is increased.(6) DP of MMA graft polymer increases nearly parallel to the increase in the amount of graft with reaction time. The minimum of DP curve of ultimate graft polymer with respect to the initiator or nitric acid concentration, corresponds nearly to the maximum of the related graft amount curve.(7) The apparent activation energies obtained are MA6.7, EA8.5, MMA8.2, and AN 10.1 kcal/mol.(8) Atmosphere in the reaction vessel controlls the monomer vapour diffusion by the pressure variation and retards the grafting by oxygen in air. If air is replaced by nitrogen, graft amount of MA or EA increases several folds, but that of MMA or AN does not.(9) The breaking load of the grafted rayon is almost constant, the extension increases slightly, the initial modulus of MA or EA grafted decreases slightly, that of MMA or AN grafted increases slightly with graft amount.